There are many; see, for example, Simon [1]}, [2]}. Here is the simplest,
due to Deift [3]}, [4]}: If \(\sigma \)  is the spectrum of an operator
\( \sigma (C\!D)\setminus \lbrace 0\rbrace =\sigma (DC)\setminus \lbrace 0\rbrace \) 
so with \(\sigma _r\)  the spectral radius,
\( \sigma _r(C\! D) = \sigma _r(DC)\le \Vert DC\Vert \) 
If \(C\! D\)  is selfadjoint, \(\sigma _r (C\! D)=\Vert C\! D\Vert \) , so
\( C\! D\text{ selfadjoint} \Rightarrow \Vert C\! D\Vert \le \Vert DC\Vert \) 
Thus,
\( \Vert e^{-A/2} e^{-B/2}\Vert ^2 = \Vert e^{-B/2} e^{-A} e^{-B/2}\Vert  \le \Vert e^{-A} e^{-B}\Vert \) 
By induction,
\( \Vert (e^{-A/2^n} e^{-B/2^n})^{2^n}\Vert  \le \Vert e^{-A/2^n} e^{-B/2^n}\Vert ^{2n}\le \Vert e^{-A} e^{-B}\Vert \) 
Take \(n\rightarrow \infty \)  and use the Trotter product formula to get (REF ).
